Lecture Room: | 115 Van Hise |
Lecture Time: | 9:30–10:45 TuTh |
Lecturer: | Jean-Luc Thiffeault |
Office: | 503 Van Vleck |
Email: | |
Office Hours: | Tue 12:15–13:00, Thu 8:30–9:15 |
The final exam is on Thursday December 20 at 2:45pm. It
will last 2 hours. The exam will consist of (about) 4 questions.
You are responsible for all the material in the class, except as
noted below, but the exam will lean heavily on the post-midterm
parts.
Here is a not-completely-exhaustive list of what you're expected to know:
See the official syllabus.
The textbook for the class is Nonlinear Dynamics and Chaos by Steven Strogatz (Second Edition).
Math 319 or 320, or consent of instructor.
Every two weeks or so I will assign homework from the textbook and post it here.
HW 1 (Due Sept 25): 2.1: 1–4; 2.2: 1–4, 7, 10, 13; 2.3: 1, 4; 2.4: 1, 3, 6, 9; 2.5: 1, 2, 4, 6; 2.7: 1, 3. Solutions
HW 2 (Due Oct 9): 3.1: 1, 2; 3.2: 1, 2, 4; 3.3: 1 [except (d)]; 3.4: 1 (note: r x + 4x^{3}), 2, 4, 5, 7, 10, 11, 15; 3.5: 2, 3, 6 [except (e)]; 3.6: 2, 4. Solutions
HW 3 (Due Oct 23): 3.7: 1–4. 5.1: 3–6, 9, 10; 5.2: 1–4, 7, 10, 11, 13. Solutions
HW 4 (Due Nov 6): 6.1: 1, 2, 4, 6; 6.2: 2; 6.3: 1, 2, 4, 5, 9 (except (e)), 11, 13; 6.4: 3, 4. [6.3.2, 6.3.5: OK in this case to assume centers persist.] Solutions
HW 5 (Due Nov 20): 6.5: 1, 2, 3, 11, 19; 6.7: 2 [except the 'reversible' question in (c)]; 6.8: 1, 3, 4, 5, 6, 8; 7.1: 1, 4, 8; 7.2: 2, 6, 10, 14; 7.3: 1, 3, 4. Solutions
HW 6 (Due Dec 11): 9.2: 1, 2 [except 'stiffer challenge']; 10.1: 10, 11; 10.3: 1, 4, 5, 7. Solutions [Correction: 10.1.11 x=0 should be unstable.]
We'll use Canvas discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web.
lecture | date | sections | topic |
1 | 09/06 | 1 | Introduction |
2 | 09/11 | 2.1–2.4 | One-dimensional ODEs |
3 | 09/13 | 2.5–2.8 | Existence and uniqueness |
4 | 09/18 | – | Modeling hagfish slime [Matlab code] |
5 | 09/20 | – | Hagfish (cont'd) |
6 | 09/25 | 3.1 | Saddle-node bifurcations |
7 | 09/27 | 3.2–3.4 | Transcritical and pitchfork bifurcations |
8 | 10/02 | 3.5 | Overdamped bead |
9 | 10/04 | 3.6 | Imperfect bifurcations; catastrophes |
10 | 10/09 | 3.7 | Insect outbreak |
11 | 10/11 | 5.1 | Two-dimensional linear flows |
12 | 10/16 | 5.2 | Two-dimensional linear flows (cont'd) |
13 | 10/18 | 5.2 | Two-dimensional linear flows (finish) |
14 | 10/23 | 6.1–6.2 | Phase plane |
15 | 10/25 | 6.3–6.4 | Linearization; Lotka–Volterra model |
– | 10/30 | – | MIDTERM [mean 70%; solutions] |
16 | 11/01 | 6.4–6.5 | Lotka–Volterra model; Conservative systems |
17 | 11/06 | 6.7 | Pendulum |
18 | 11/08 | 6.8 | Index theory |
19 | 11/13 | 7.1–7.2 | Limit cycles |
20 | 11/15 | 7.2–7.3 | Lyapunov functions; Poincaré–Bendixson Theorem |
21 | 11/20 | 9.2–9.3 | The Lorenz equations (Lorenz's paper) (Matlab files) |
22 | 11/27 | 10.0–10.1 | One-dimensional maps |
23 | 11/29 | 10.2–10.3 | Logistic map |
24 | 12/04 | 10.3–10.4 | Periodic orbits of maps; Chaos (Matlab files) |
25 | 12/06 | 10.5 | Lyapunov exponent |
26 | 12/11 | 11.1–11.4 | Fractals |
There will be a midterm exam in class and a final exam. The final grade will be computed according to:
Homework | 35% |
Midterm exam | 30% |
Final exam | 35% |
Midterm exam | Tue Oct 30, 2018 at 9:30–10:45 | (in class) |
Final exam | Thu Dec 20, 2018 at 14:45–16:45 | (room SOC SCI 6203) |